Answer:
The area of the shelf is 86.59 square inches
Step-by-step explanation:
The formula of the area of the circle is A = π r², where
- r is the radius of the circle
∵ The corner shelf is [tex]\frac{1}{4}[/tex] of a circle
→ That means its area is [tex]\frac{1}{4}[/tex] the area of the circle
∴ The area of the corner shelf = [tex]\frac{1}{4}[/tex] × area of the circle
∵ Area of the circle = π r²
∴ The area of the corner shelf = [tex]\frac{1}{4}[/tex] × π r²
∵ The radius of the shelf is 10.5 inches
∴ r = 10.5 inches
→ Substitute the values of r in the formula of the area
∴ The area of the corner shelf = [tex]\frac{1}{4}[/tex] × π × (10.5)²
∴ The area of the corner shelf = 86.59014751
→ Round it to the nearest hundredth
∴ The area of the corner shelf = 86.59 square inches
∴ The area of the shelf is 86.59 square inches
